Robust H_∞ Filtering For Networked Systems Via Delta Operator

With the continuous development of computer networks and communication technology, control theory has been given higher requirements. Ubiquitous mobile network, the widespread use of intelligent equipment, as well as the actual demand of controlling system laid the foundation of the networked control systems. When the control system is transmitting information and signals, it enables different controlled objects with various performance to exchange data within the network, which is an indication of the characterization of advanced control systems, namely, networking and intelligentizing. Compared to the classical Kalman filter, however, H_∞ filtering method possesses better performance dealing with systematic uncertainties in reality. It is also propitious to achieve the control strategy to conduct the state estimate for the networked systems with H_∞ filtering. Additionally, the Delta operator method can not only put both discrete and continuous system models into a unified frame, it can also preferably solve the ill condition problems caused by traditional shift operator in its high-speed sampling. Therefore, to analyze the robust filtering problem of uncertainty in networked systems via Delta operator discretization method has important application value and practical significance.Based on Delta operator, the problems of robust H_∞ filter in networked control systems which have time-delay and data dropout are discussed in this thesis. By using time delay system theory and switched systems theory, the system models are established. The H_∞ filters which satisfy the robust performance are designed. The main works in the thesis are as follows:Firstly, the problem of H_∞ filtering for delta operator formulated systems with time-varying delays and uncertainties is considered. Uncertainties which exist in state matrices and satisfy the norm-bounded condition are structured. Based on time-delay system theory, the system model is established. The robust H_∞ performance analysis of filtering-error system is proposed by using a Lyapunov-Krasovskii functional via delta operator, Matrices inequalities are inverted to linear matrices inequalities by Schur complement, the sufficient conditions make the system stability and the performance index are obtained by solving linear matrix inequalities, and the robust H_∞ filter design method is also obtained.Secondly, considered the uncertain networked systems with data dropout, we established the system model using switched systems theory via Delta operator. With data dropout or no dropout loss cases, systems were established for the two subsystems. And error system is established as a discrete-time switched system which having two subsystems. A sufficient condition which makes the filtering error system satisfy the exponential stability and robust H_∞ performance is given by solving a set of linear matrix inequality, and the filter parameter is also obtained.Finally, numerical simulations are conducted by using Matlab LMI toolbox for the filtering method in this thesis, which verifies the feasibility and the effectiveness of the robust H_∞ filter we designed. And the state of the signal is also estimated.